Local boundedness of weak solutions to elliptic equations under unbalanced Orlicz growth conditions

TL;DR

This paper proves local boundedness of weak solutions to nonlinear elliptic equations with unbalanced Orlicz growth, broadening understanding beyond standard symmetric growth conditions.

Contribution

It introduces new sufficient conditions for boundedness in non-variational elliptic equations with distinct Young functions, extending existing $p,q$-growth results.

Findings

Established local boundedness under unbalanced Orlicz growth conditions.

Extended results to include and surpass known $p,q$-growth cases.

Provided a non-variational framework without symmetry assumptions.

Abstract

We establish sufficient conditions for the local boundedness of weak solutions to a broad class of nonlinear elliptic equations in divergence form, under unbalanced growth conditions on the stress field. Our analysis is carried out in a non-variational setting, with no symmetry or structural assumptions on the operator. The ellipticity and growth are prescribed via distinct Young functions, leading to a Orlicz-type setting that captures a wide class of nonstandard behaviors. As a special case, the theory encompasses and extends the known results on equations with $p,q$-growth.